# Month: June 2021

## Graphing a Reciprocal Function

There are a number of standard techniques for graphing functions, such as transforming simple functions, or finding asymptotes and holes for rational functions, and using calculus to find slopes. What if you have a rational function of a trig  function, and can’t yet use calculus to figure it out? We’ll look at how we can …

## A Random Walk on a Graph

(A new question of the week) It seems that most of the interesting questions recently have been about relatively advanced topics, though commonly in introductory classes. Here, we’ll help a student think through a problem introducing the idea of a random walk on a graph. (“Graph” here doesn’t mean the graph of an equation, which …

## Proving Two Groups are Isomorphic

(A new question of the week) Two weeks ago, in Proving Certain Polynomials Form a Group, we joined a beginner in learning about groups. Here we will pick up where that left off, learning how to prove that the group we saw there, a subset of polynomials, is isomorphic to a group of matrices. As …

## Filling a Cistern: Three Pipes, No Numbers

(A new question of the week) Today we’ll look at a classic algebra word problem: Finding how long it takes to fill a cistern through two pipes, with a drain open. But usually these problems are given with specific numbers, as a simple exercise in algebra. What if it’s all variables? the discussion provides some …